Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus

Akihiko Takahashi and Toshihiro Yamada ()
Additional contact information
Akihiko Takahashi: The University of Tokyo
Toshihiro Yamada: Hitotsubashi University

Partial Differential Equations and Applications, 2023, vol. 4, issue 4, 1-31

Abstract: Abstract This paper proposes a new spatial approximation method without the curse of dimensionality for solving high-dimensional partial differential equations (PDEs) by using an asymptotic expansion method with a deep learning-based algorithm. In particular, the mathematical justification on the spatial approximation is provided. Numerical examples for high-dimensional Kolmogorov PDEs show effectiveness of our method.

Keywords: Asymptotic expansion; Deep learning; Kolmogorov PDEs; Malliavin calculus; Curse of dimensionality; 35C20; 60H07; 68T07 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s42985-023-00240-4 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:pardea:v:4:y:2023:i:4:d:10.1007_s42985-023-00240-4

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/42985/

DOI: 10.1007/s42985-023-00240-4

Access Statistics for this article

Partial Differential Equations and Applications is currently edited by Zhitao Zhang

More articles in Partial Differential Equations and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().